KIEV, May 4 (Reuters) - Ukrainian Prime Minister Arseny Yatseniuk accused Russia on Sunday of engineering clashes in Odessa that led to the deaths of more than 40 pro-Russian activists in a blazing building and pushed the country closer to civil war.

Yatseniuk, speaking in Odessa, attacked police forces in the Black Sea port city, suggesting they were more interested in the fruits of corruption than maintaining order. Had they done their job, he said, "these terrorist organisations would have been foiled".

Friday's clashes were the most deadly since Moscow-oriented president Viktor Yanukovich was forced to flee in February and pro-Russian militants launched uprisings in the industrial east. They also marked the first serious disorder outside eastern areas since Yanukovich fell, heralding possible future trouble for Kiev.

"There were dozens of casualties resulting from a well-prepared and organised action against people, against Ukraine and against Odessa," Yatseniuk told representatives of social organisations.

He dismissed Russian accusations that his government was provoking bloodshed in the east with an operation to restore Kiev's authority in a series of cities under rebel control.

"The process of dialogue had begun, only it was drowned out by the sound of shooting from automatic rifles of Russian production," he said.

The former Soviet republic of Ukraine is divided between a largely Russian-speaking population in the industrial east and Ukrainian-speaking west, where more pro-European Union views prevail. Moscow says Russian-speakers face threats from Ukrainian nationalist militants, an accusation Kiev denies.

THE "SEVENTH KILOMETRE"

Odessa was quiet on Sunday. Flowers were laid outside the burnt-out stone building of the trade union organisation guarded by police. On social networking sites, pro-Russian activists called for a gathering on the "Kulikovo Field", a large square that was the focus of Friday's fighting, Interfax-Ukraine agency said.

The deaths occurred after running clashes, involving petrol bombs and gunfire, between supporters and opponents of Moscow on the streets of Odessa, which has a mixed population of Russian and Ukrainian speakers.

A Reuters correspondent reported shooting on Sunday on the road between the eastern towns of Kharkiv and Izyum where Ukrainian forces took over a checkpoint.

There were no signs of Ukrainian forces pushing their declared campaign to remove separatists from eastern cities including Kramatorsk, Donetsk and the rebel stronghold of Slaviansk.

Kiev is organising national elections for May 25. However, as things stand, it would have trouble conducting the vote in many parts of the east, a circumstance that would allow Russia to declare any government emerging as bereft of legitimacy.

Russia denies ambitions to seize eastern Ukraine as it has annexed the Crimean peninsula but reserves the right to send troops to defend Russian-speakers if it deems necessary.

Separatists who have declared a "People's Republic of Donetsk" are planning a referendum on secession on May 11.

Yatseniuk, whose government Moscow refuses to recognise, said there would be sackings in the Odessa interior forces.

"If the law enforcement system in Odessa had worked not exclusively on the 'Seventh Kilometre' and had protected people, then these terrorist organisations would have been foiled."

The Seventh Kilometre is an open market on the edge of Kiev associated in the popular consciousness with corruption and black market business. Yatseniuk's comments reflect a broader concern about the reliability of Ukraine's security forces.

The capital Kiev has remained quiet since the protests that forced Yanukovich to flee to Russia. But celebrations this week marking the anniversary of victory in World War Two could be a source of tension. (writing by Ralph Boulton; editing by David Stamp)

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